Article

The Dynamics of Leveraged and Inverse Exchange-Traded Funds

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Abstract

Leveraged and inverse Exchange-Traded Funds (ETFs) have attracted significant assets lately. Unlike traditional ETFs, these funds have “leverage” explicitly embedded as part of their product design. While these funds are primarily used by short-term traders, they are gaining popularity with individual investors placing leveraged bets or hedging their portfolios. The structure of these funds, however, creates both intended and unintended characteristics that are not seen in traditional ETFs. This note provides a unified framework to better understand the underlying dynamics of leveraged and inverse ETFs, their impact on market volatility and liquidity, unusual features of their product design, and questions of investor suitability. We show that the daily re-leveraging of these funds can exacerbate volatility towards the close. We also show that the gross return of a leveraged or inverse ETF has an embedded path-dependent option that under certain conditions can lead to value destruction for a buy-and-hold investor. The unsuitability of these products for longer-term investors is reinforced by the drag on returns from high transaction costs and tax inefficiency.

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... For instance, if the Russell 1000 Financial Services Index increases by 1%, the rebalancing demand of LETFs totals roughly 2% of the daily volume for an average financial stock. Furthermore, academic studies ( Cheng and Madhavan, 2009;Bai et al., 2012) and anectodal reports 12 suggest that LETFs rebalance their portfolio in the last hour of trading. Therefore, a large market move could make these stocks vulnerable near the market close, or even before to the extent that opportunistic traders react in anticipation of subsequent LETF rebalancing. ...
... Trainor (2010) cannot find evidence that suggests Leveraged ETFs increase volatility. Focusing on the S&P 500 index returns and aggregate LETF rebalancing demands, Cheng and Madhavan (2009) argue that aggregate LETF rebalancing demand has price pressure on the end-ofday S&P 500 index returns. Similarly, Bai et al. (2012) examine the impact of 6 LETFs on 63 real estate sector stocks and find evidence for both end-of-day LETF price pressure and extra volatility. ...
... Generating a multiple of daily index return requires LETFs to sell when the market is down and buy when the market is up, resulting in transaction costs. Several studies (Jarrow (2010); Cheng and Madhavan (2009); Huang and Guedj (2009)) show that returns of LETFs could be significantly different that their multiple of target index returns for holding periods longer than one day. The investment horizon of a retail trader is typically longer than a day, suggesting that LETFs may not be suitable for many retail investors. ...
... Commentators have referred to them as "weapons of mass destruction" and claim that they pose "serious threats to market stability" because they "have turned the market into a casino on steroids." 1 Others have claimed that leveraged ETFs "could send volatility through the roof, and prices through the floor [.]" 2 It appears as though policy makers are also concerned about these products, as the Securities and Exchange Commission (SEC) has issued a moratorium on approving exemptive requests for new leveraged and inverse ETFs. 3 The basis of the commentators' concerns seems to be a common perception that leveraged and inverse ETFs must rebalance their portfolios in the same direction as the contemporaneous return on their underlying assets in order to maintain a constant leverage ratio. Conventional thinking suggests that by purchasing assets following positive returns and selling assets following negative returns, these types of financial products exert additional upward price pressure on the underlying assets following positive returns and additional downward pressure following negative returns (see, e.g., Cheng and Madhavan (2009), Bai, Bond, and Hatch (2014), Tuzun (2014), and Shum et al. (2014)). However, such reasoning is incomplete because it overlooks the effects of capital flows. ...
... None of these analyses, however, use actual data on ETF holdings or rebalancing activity to estimate the impact of ETFs on volatility. Instead, many of these studies rely on an equation derived by Cheng and Madhavan (2009) to calculate "hypothetical" rebalancing by ETFs, and they do not take into account the effect of capital flows. ...
... ETFs rebalance in the same direction as the index return because these ETFs must increase (decrease) their exposure when the return is positive (negative), whereas inverse ETFs rebalance in the same direction as the index return because these ETFs must decrease (increase) their negative exposure when the return is positive (negative). Rebalancing processes similar to (6) have been derived by Cheng andMadhavan (2009) andJarrow (2010), though these authors ignore the effects of capital flows. ...
... Consequences of daily rebalancing have been intensively studied in the literature. Cheng and Madhavan (2009) suggested a unified framework explaining the return dynamics of leveraged and inverse ETFs. Tang and Xu (2013) attempts at explaining deviations that remain after netting out the compounding effect. ...
... For β = −2 and β = 3, the term β − β 2 = −6, similarly for β = −1 and β = 2, the term β − β 2 = −2 explaining the reason behind the same values of the -2xLETF and +3xLETF, and the -1xLETF and +2xLETF on even days. Cheng and Madhavan (2009) observed the same relationship when calculating the amount by which the exposure of the total return swaps that need to be adjusted or re-hegded. The above analysis shows that for a mean reverting ETF, the Leveraged ETF will suffer from a loss in value regardless of the multiplier direction. ...
... The forecast error of the QQQ ETF is much smaller than any other index, the result could be attributed to its smaller data relative to the other indexes, contradicting Enders (1995) assumption. In order to further probe the enhanced ability of ARIMA models to forecast with smaller data sets, ARIMA(p,d,q) models are fitted to S&P500 data during varying time frames, from September 2 nd , 2000,2009, 2010, 2011, 2012until April 13 th , 2016 ARIMA models for the five different time frames. The forecasts are for 100 points ahead in time i.e. until September 2 nd , 2016. ...
... Consequences of daily rebalancing have been intensively studied in the literature. Cheng and Madhavan (2009) suggested a unified framework explaining the return dynamics of leveraged and inverse ETFs. Tang and Xu (2013) attempts at explaining deviations that remain after netting out the compounding effect. ...
... For β = −2 and β = 3, the term β − β 2 = −6, similarly for β = −1 and β = 2, the term β − β 2 = −2 explaining the reason behind the same values of the -2xLETF and +3xLETF, and the -1xLETF and +2xLETF on even days. Cheng and Madhavan (2009) observed the same relationship when calculating the amount by which the exposure of the total return swaps that need to be adjusted or re-hegded. The above analysis shows that for a mean reverting ETF, the Leveraged ETF will suffer from a loss in value regardless of the multiplier direction. ...
... The forecast error of the QQQ ETF is much smaller than any other index, the result could be attributed to its smaller data relative to the other indexes, contradicting Enders (1995) assumption. In order to further probe the enhanced ability of ARIMA models to forecast with smaller data sets, ARIMA(p,d,q) models are fitted to S&P500 data during varying time frames, from September 2 nd , 2000,2009, 2010, 2011, 2012until April 13 th , 2016 ARIMA models for the five different time frames. The forecasts are for 100 points ahead in time i.e. until September 2 nd , 2016. ...
... Curcio, Anderson, and Guirguis [2014a] also found a significant increase in the stock price volatility of banks and other financials emanating from the inception of the first-ever, purely financial ETF, and especially from the introduction of the first-ever purely financial, leveraged and inverse ETFs. In the only other study pertaining to volatility on leveraged ETFs, Cheng and Madhavan [2009] show, through limited empirical results, that the daily rebalancing of leveraged ETFs, which occurs near the close of trading, can exacerbate late-day volatility for large-capitalization indexes. ...
... of their stated daily objectives. Cheng and Madhavan [2009], through a mathematical analysis of return dynamics for leveraged ETFs, conclude that buy-andhold investing in leveraged ETFs, under volatile conditions in the benchmark index, can lead to eventual value destruction. 3 But do these dire warnings overstate the case? ...
... Thus, should investors in the broad market restrict their use of leveraged ETFs to single-day holding periods? Cheng and Madhavan [2009] show mathematically that the gross return of a leveraged long or inverse ETF has an embedded path-dependent option that under specific conditions can lead to value destruction for a buy-and-hold investor. Are such value-destroying price paths and conditions common and inevitable for all underlying leveraged ETF reference indexes? ...
... First, the longevity of a levered or inverse ETP depends critically on the expected return and volatility of the fund's index. In their foundational work on levered funds, Cheng and Madhavan (2009) show analytically that if the expected return of the benchmark index is positive, inverse and levered inverse funds will eventually fail (i.e., their expected values are zero). Conversely, if the expected benchmark return is negative, long and levered long funds will fail. ...
... If the benchmark index has risen over the day, the issuers of the levered and inverse funds must buy more swaps or futures to re-hedge their position, which, in turn, drives the index upward, which, in turn, drives more buying. As noted by Cheng and Madhavan (2009), this negative feedback loop is inherently destabilizing. Finally, the realized daily ETP return will be different from its levered benchmark return for a variety of reasons including expense ratios, basis risk, and contract indivisibilities. ...
... This, too, contributes to the basis risk between NAV and the benchmark.End-of-day rebalancing costs contribute to the basis risk between the NAV and the benchmark in at least two ways. Again, the work ofCheng and Madhavan (2009) comes to bear. Levered and inverse funds create end-of-day rebalancing needs-needs that can only be managed risklessly if the hedge transaction is consummated at exactly the NAV.CM focus in on return swaps, as they are the primary hedge instrument for security index ETFs. ...
Article
Full-text available
Levered and inverse ETPs are designed to provide geared long and short exposures to the daily returns of different benchmark indexes. The benchmarks can be any reference index. The popular ones are on stocks, bonds, commodities and volatility. The problem with these products is that they are not generally well-understood. They are neither suitable buy-and-hold investments nor effective hedging tools. They are unstable and exist only as a mechanism for placing short-term directional bets. But, if that is their sole purpose, how is society better served? Traditionally, securities markets have existed as a means of capital formation and price discovery. The objective of this paper is to explain the mechanics of levered and inverse ETP returns, simulate their expected return performance based on the most popular benchmarks, and document the actual performance of 35 popular products.
... The longevity of a levered or inverse ETP depends critically on the expected return and volatility of the fund's benchmark index. Cheng and Madhavan (2009) showed analytically that (1) if the expected return of the benchmark index is positive, inverse and levered inverse funds will eventually fail (i.e., their expected values are zero) and (2) if the expected benchmark return is negative, long and levered long funds will fail. We have extended these results in three important ways. ...
... Second, Cheng and Madhavan (2009) dismissed the negative expected index returns they found by saying that it "seems unlikely in a long-run equilibrium, but it is included for completeness" (p. 56). ...
... First, a levered and inverse fund must rebalance its derivatives position at the end of day in order to deliver its promised levered return on the following day. For security indexes, the rebalancing is accomplished by using total-return swaps, as pointed out by Cheng and Madhavan (2009). Because these trades are OTC trades, basis risk can be minimized since the timing of the swap trade is unencumbered by exchange hours and can be negotiated when settlement prices are known. ...
Article
Levered and inverse exchange-trade products (ETPs) are designed to provide geared long and short exposures to the daily returns of various benchmark indexes. The benchmarks may be any reference index, but the popular ones are indexes of stocks, bonds, commodities, and volatility. The problem with these products is that they are not generally well understood, particularly those with futures-based benchmarks. Levered and inverse ETPs are neither suitable buy-and-hold investments nor effective hedging tools. They are unstable and exist only as mechanisms for placing short-term directional bets. Levered and inverse products are not, and cannot be, effective investment management tools.
... ere have been some empirical studies reporting that a leveraged ETF affects the underlying asset markets [2][3][4][5][6]. Chen and Madhavan [2] suggested that by purchasing assets following positive returns and selling assets following negative returns, leveraged ETFs exert additional upward price pressure on the underlying assets following positive returns and additional downward pressure following negative returns, both of which amplify market movements. ...
... ere have been some empirical studies reporting that a leveraged ETF affects the underlying asset markets [2][3][4][5][6]. Chen and Madhavan [2] suggested that by purchasing assets following positive returns and selling assets following negative returns, leveraged ETFs exert additional upward price pressure on the underlying assets following positive returns and additional downward pressure following negative returns, both of which amplify market movements. Rompotis [5] examined how UK leveraged ETFs affected their underlying indexes and found that they could perform their daily rebalancing trades correctly but tracking errors-which refers to the divergence between the daily return of the leveraged ETF and the leverage ratio of the ETF times the corresponding return of underlying asset-became larger as market volatility increased. ...
Article
Full-text available
A leveraged ETF is a fund aimed at achieving a rate of return several times greater than that of the underlying asset such as Nikkei 225 futures. Recently, it has been suggested that rebalancing trades of a leveraged ETF may destabilize the financial markets. An empirical study using an agent-based simulation indicated that a rebalancing trade strategy could affect the price formation of an underlying asset market. However, no leveraged ETF trading method for suppressing the increase in volatility as much as possible has yet been proposed. In this paper, we compare different strategies of trading for a proposed trading model and report the results of our investigation regarding how best to suppress an increase in market volatility. As a result, it was found that as the minimum number of orders in a rebalancing trade increases, the impact on the market price formation decreases.
... The LETPs' compounding deviation due to "constant leverage trap" was the center of investor lawsuits, regulator warnings, and negative media attention after the global financial crisis. Recent literature on LETPs examine this "constant leverage trap" in detail and demonstrate its impact on the tracking performance of stock-based LETPs (Cheng and Madhavan 2009;Avellaneda and Zhang 2010;Tang and Xu 2013;Loviscek et al. 2014) While previous studies on VIX ETPs have not considered the potential impact of the compounding effect on these products' tracking performance, this paper will examine the impact of the compounding effect along with the negative roll-yield on the tracking performance of VIX LETPs over multiple holding days. ...
... RD Compounding,t1−t2 ≡ R Target,t1−t2 -E Underlying (R t1−t2 ). The Compounding deviation is due to the daily compounding nature of leveraged ETPs and the resulted "constant leverage trap" over multiple-day horizons (Cheng and Madhavan 2009;Avellaneda and Zhang 2010;Tang and Xu 2013;Loviscek et al. 2014). In addition to the index substitution deviation and compounding deviation, fund management issues and the expense ratio will lead to the NAV deviation (RD NAV ,t1−t2 ≡ R NAV ,t1−t2 -R Target,t1−t2 ), while market inefficiency and trading frictions will lead to the efficiency deviation (RD Inefficiency,t1−t2 ≡ R ETP,t1−t2 − R NAV ,t1−t2 ). ...
Article
Full-text available
VIX exchange-traded products (ETPs) provide tracking on the return of a constant-maturity VIX futures index, instead of the uninvestable VIX spot index. In this paper, we develop a comprehensive framework to dissect the tracking performance of regular and leveraged VIX ETPs. In this framework, naïve investors in VIX ETPs expect to achieve the ETP’s leverage ratio multiplied by the VIX return during their holding period, but the actual ETP return can deviate dramatically from this naïve expected return due to four components of return deviation. The index substitution deviation is shown to be the primary driver of the bull (inverse) VIX ETPs’ return erosion (enhancement), which can be explained by the negative roll-yield as a result of the contango term structure of underlying VIX futures index. For leveraged VIX ETPs over multiple holding days, the compounding deviation due to the “constant-leverage trap” can be sizable. In addition, the NAV deviation due to expense ratio and fund management issues is negative, and the inefficiency deviation doesn’t accumulate over long holding periods due to the creation/redemption feature. Our return deviation framework can be generalized to other ETPs tracking indices that are either uninvestable or unrealistic to replicate.
... Malamud (2015) demonstrates that ETFs may create a transmission mechanism for non-fundamental shocks to the underlying securities. Cheng and Madhavan (2009) show that the returns on leveraged ETFs are path-dependent. Tuzun (2012) finds that the rebalancing of leveraged ETFs can increase the volatility of constituent stocks, whereas Ivanov and Lenkey (2018) find evidence that these effects are offset by ETF flows. ...
... (1.12) shows that leverage rebalancing exposes the ETF to variance and to squared realized returns: ∂A T ∂σ 2 < 0 and ∂ 2 A T ∂r 2 T > 0 (for low σ 2 ). 27 Previous papers on leveraged ETFs have mostly ignored the exposure to squared realized returns, and emphasized that leveraged ETFs are negatively exposed to variance (see, e.g., Cheng and Madhavan, 2009). In practice, however, the exposure is not monotonic in variance. ...
Thesis
In the first paper of my dissertation I study the size and source of exchange-traded funds’ (ETFs) price impact in the most ETF-dominated asset classes: volatility (VIX) and commodities. I show that the introduction of ETFs increased futures prices. To identify ETF-induced price distortions, I propose a model-independent approach to replicate the value of a VIX futures contract. This allows me to isolate a nonfundamental component in VIX futures prices, of 18.5% per year, that is strongly related to the rebalancing of ETFs. To understand the source of that component, I decompose trading demand from ETFs into three main parts: leverage rebalancing, calendar rebalancing, and flow rebalancing. Leverage rebalancing has the largest effects. It amplifies price changes and introduces unhedgeable risks for ETF counterparties. Surprisingly, providing liquidity to leveraged ETFs turns out to be a bet on variance, even in a market with a zero net share of ETFs. Trading against leverage rebalancing delivers large abnormal returns and Sharpe ratios above two across markets. The second paper analyses the impact of the ECB’s Corporate Sector Purchase Programme (CSPP) announcement on prices, liquidity and debt issuance in the European corporate bond market. I find that the quantitative easing (QE) programme increased prices and liquidity of bonds eligible to be purchased substantially. Bond yields dropped on average by 30 bps (8%) after the CSPP announcement. Tri-party repo turnover rose by 8.15 million USD (29%), and bilateral turnover went up by 7.05 million USD (72%). Bid-ask spreads also showed significant liquidity improvement in eligible bonds. QE was successful in boosting corporate debt issuance. Firms issued 2.19 billion EUR (25%) more in QE-eligible debt after the CSPP announcement, compared to other types of debt. Surprisingly, corporates used the attracted funds mostly to increase dividends. These effects were more pronounced for longer-maturity, lower-rated bonds, and for more credit-constrained, lower-rated firms. The third paper (co-authored with Christian Julliard, Zijun Liu, Seyed E. Seyedan and Kathy Yuan) studies the determinants of repo haircuts in the UK market. We find that transaction maturity and collateral quality have first order importance. We also document that counterparties matter in determining haircuts. Hedge funds, as borrowers, receive significantly higher haircuts. Larger borrowers with higher ratings receive lower haircuts, but we find that these effects can be overshadowed by collateral quality. Repeated bilateral relationships also matter and generate lower haircuts. We find evidence supporting an adverse selection explanation of haircuts, but limited evidence in favor of lenders’ liquidity position or default probabilities affecting haircuts.
... In practice, swaps are vastly more used, as they are more flexible than futures because futures require standard amounts and expiration time (Rompotis, 2014). Also futures are more limited in terms of index representation, and the risk related to imperfect hedging is significantly higher than with total return swaps (Cheng & Madhavan, 2009). ...
... This observation, although peculiar for some investors, is just the effect of employing daily replication strategies from leveraged funds. As we see in extremely high volatile paths, leveraged ETFs tend to underperform greatly even in short periods of time; this phenomenon is described in academic literature as volatility decay (Avellaneda & Zhang, 2010;Cheng & Madhavan, 2009;Guo & Leung, 2014). ...
Article
Full-text available
Leveraged Exchange Traded Funds (ETFs) (LETFs) are a recent and highly successful financial innovation; yet, investors and several studies criticized them for not performing as advertised, especially in the long term. Τhis paper discusses their unique characteristics and their path-dependent price dynamics, which may result in unexpected returns. Furthermore, the authors evaluate the performance of a large sample of European and American leveraged ETFs since each fund’s inception and show that they perform as intended for daily holding periods. Leveraged ETFs are also successful in delivering the promised performance over holding periods of up to one week, their performance starts to deviate when the holding period increases to one month. Empirical evidence suggests that bear (short) ETFs deviate from their target return more quickly than their bull (long) counterparts as the holding period lengthens. A possible explanation for this is that transaction costs, which are related to daily re-balancing activity, are higher for bear funds. When comparing the daily performance of European vs American funds, the authors find them both to be equally efficient in replicating their benchmarks, although European leveraged ETFs are much smaller in their Assets Under Management (AUM) compared to US LETFs.
... Case et al. (1991) state that a short position on conventional REITs cannot be used as means of hedging real estate exposure because there are just not enough REIT shares available for hedging. Cheng and Madhavan (2009) suggested that inverse ETFs could provide another mean to hedge real estate exposure. Using inverse ETFs an investor can get short exposure to the underlying index returns. ...
... The larger is the fundamental difference between the asset and the derivative, the more likely it is that the basis risk materializes. (Cheng and Madhavan 2009.) Due to aforementioned obstacles in the utilization of real estate derivatives, cross-hedging with a suitable instrument should be considered if real estate exposure needs to be hedged. ...
Preprint
Full-text available
Based on quarterly data from the US commercial real estate market we find that a short position on the Dow-Jones US Real Estate index (DJUSRE) can serve as a useful and effective hedge against the price risk of U.S. direct commercial real estate investments. According to our results, when utilizing the DCC-GARCH-models in the empirical analysis, compared to hedging with the stock market related VIX derivatives, especially hedging with DJUSRE would have decreased the price deterioration of U.S. direct real estate portfolios during the global financial crisis when compared to an unhedged position. In contrast to using DJUSRE, we find that the hedging effectiveness of VIX against direct real estate exposure is trivial. Hence, we are able to conclude that at least for the lower frequency, like quarterly market observations, VIX cannot be considered as a useful nor effective hedge against adverse price movements of direct commercial real estate investments, so the standard stock market hedge instruments do not provide a safety net for hedging against the price risks in the U.S. real estate markets at all.
... ere have been some empirical studies reporting that a leveraged ETF affects the underlying asset markets [2][3][4][5][6]. Chen and Madhavan [2] suggested that by purchasing assets following positive returns and selling assets following negative returns, leveraged ETFs exert additional upward price pressure on the underlying assets following positive returns and additional downward pressure following negative returns, both of which amplify market movements. ...
... ere have been some empirical studies reporting that a leveraged ETF affects the underlying asset markets [2][3][4][5][6]. Chen and Madhavan [2] suggested that by purchasing assets following positive returns and selling assets following negative returns, leveraged ETFs exert additional upward price pressure on the underlying assets following positive returns and additional downward pressure following negative returns, both of which amplify market movements. Rompotis [5] examined how UK leveraged ETFs affected their underlying indexes and found that they could perform their daily rebalancing trades correctly but tracking errors-which refers to the divergence between the daily return of the leveraged ETF and the leverage ratio of the ETF times the corresponding return of underlying asset-became larger as market volatility increased. ...
Preprint
Full-text available
A leveraged ETF is a fund aimed at achieving a rate of return several times greater than that of the underlying asset such as Nikkei 225 futures. Recently, it has been suggested that rebalancing trades of a leveraged ETF may destabilize the financial markets. An empirical study using an agent-based simulation indicated that a rebalancing trade strategy could affect the price formation of an underlying asset market. However, no leveraged ETF trading method for suppressing the increase in volatility as much as possible has yet been proposed. In this paper, we compare different strategies of trading for a proposed trading model and report the results of our investigation regarding how best to suppress an increase in market volatility. As a result, it was found that as the minimum number of orders in a rebalancing trade increases, the impact on the market price formation decreases.
... There are a number of studies on the price dynamics of LETFs in general, including Cheng and Madhavan (2009), Avellaneda and Zhang (2010) and Jarrow (2010). They illustrate how the return of an LETF can erode proportional to the leverage ratio as well as the realized variance of the reference index. ...
... +3x -3x). Actually, both follow a constantly declining price action procedure and this strange behavior, explained statistically by local-stochastic volatility models; see Cheng and Madhavan (2009); and Avellaneda and Zhang (2010), is a typical technical market anomaly. ...
Article
Full-text available
In investment and trading, different CSR/CSE (Corporate Social Responsibility/Corporate Social Entrepreneurship) moral ethical firms, categorized in a number of groups, may be suitable for different financial instruments (i.e. USA sector ETFs) and different market volatility situations. For the purpose of this article we first (i) analyze the trading return performance of four CSR/CSE categories (in particular: green building, green products, green services, and green transportation); and then (ii) examine and comment the correlation between the market performance of a number of firms belonging in these four CSR/CSE categories and historical ETF market volatility. Finally, we (iii) suggest CSR firms as trading tools according to dominant market volatility. Other CSR/CSE categories (like: sustainability, executive sustainability, renewable energy, green IT, green ICT, etc.) would be examined in future research by following the introduced by this paper approach. Paper concludes that, in relatively less volatile markets the Green Transportation CSR/CSE ethical firms display better results. On the other hand, in strong market volatile situations it is better to trade Green Products CSR/CSE and Green Services CSR/CSE ethical firms. Finally, the Green Building CSR/CSE ethical firms are uncorrelated with the market volatility, as well as their performance is poor in all market cases.
... Some passive investment strategies may amplify price volatility for the assets they hold because these strategies require portfolio managers to trade in the same direction as recent market moves, even in the absence of investor flows. Cheng and Madhavan (2009) and Tuzun (2014) show that leveraged and inverse ETFs (LETFs, or "geared" ETFs) -which seek daily returns that are, respectively, positive and negative multiples of an underlying index return -both must trade in the same direction as market moves that occurred earlier in the day. 19 That is, geared passive investment strategies cause both types of LETFs to buy assets (or exposures via swaps or futures) on days when asset prices rise and sell when the market is down. ...
... +3x -3x). Actually, both follow a constantly declining price action procedure and this strange behavior, explained statistically by local-stochastic volatility models; see Cheng and Madhavan (2009); and Avellaneda and Zhang (2010), is a typical technical market anomaly. ...
Article
Full-text available
In investment and trading, different CSR moral ethical firms, categorized in a number of groups, may be suitable for different financial instruments (i.e. USA sector ETFs) and different market volatility situations. For the purpose of this article we first (i) analyze the trading return performance of four CSR categories (in particular: activism, community development, corporate governance, and environment); and then (ii) examine and comment the correlation between the market performance of a number of firms belonging in these four CSR categories and historical ETF market volatility. Finally, we (iii) suggest CSR firms as trading tools according to dominant market volatility. Other CSR categories (like: fair trade & supply chain, green building, philanthropy & corporate contributions, etc.) would be examined in future research by following the introduced by this paper approach. Paper concludes that, in relatively less volatile markets the Environment CSR ethical firms display better results. On the other hand, in strong market volatile situations it is better to trade Community Development CSR and Corporate Governance CSR ethical firms. Finally, the Activism CSR ethical firms are uncorrelated with the market volatility, as well as their performance is poor in all market cases.
... For example, leveraged ETFs were blamed in the 1% run-up in the last 18 minutes of trade of the S&P 500 on October 10, 2011, despite the absence of any news (Sorkin 2011). According to Cheng & Madhavan (2009), the dynamics of leveraged ETFs lead to same-direction rebalancing (even for bear funds), akin to portfolio insurance. They also argue that short-term speculators are attracted to these products because they allow traders to make short-term, highly leveraged bets. ...
Article
Full-text available
Over nearly a quarter of a century, exchange-traded funds (ETFs) have become one of the most popular passive investment vehicles among retail and professional investors because of their low transaction costs and high liquidity. By the end of 2016, the market share of ETFs exceeded 10% of the total market capitalization traded on US exchanges, representing more than 30% of overall trading volume. ETFs revolutionized the asset management industry by taking market share from traditional investment vehicles such as mutual funds and index futures. Because ETFs rely on arbitrage activity to synchronize their prices with the prices of the underlying portfolio, trading activity at the ETF level translates to trading of the underlying securities. Researchers have found that although ETFs enhance price discovery, they also inject nonfundamental volatility into market prices and affect the correlation structure of returns. Furthermore, ETFs impact the liquidity of the underlying portfolios, especially during events of market stress.
... A number of market observations suggest that LETFs suffer from the volatility decay effect, which reflects the value erosion proportional to the realized variance of the reference index. Recent studies, including Avellaneda & Zhang (2010), Cheng & Madhavan (2009), Leung & Ward (2015), and Leung & Santoli (2016), present discrete-time and continuous-time stochastic frameworks to illustrate the path dependence of LETFs on the reference, including the volatility decay effect that is exacerbated over time. To address this issue, Leung & Santoli (2012) derived the admissible holding horizons for LETFs with respect to different risk measures. ...
... For instance, the average of annual volatility of S&P500 is 16% between 1966 and 2015, and it is 25% in the period of 2006 and 2010. 4 These large values of volatility may be explained by the leverage multiplier and the volatility of the underlying asset (Cheng and Madhavan 2009). ...
Article
This paper studies the risk assessment of semi-nonparametric (SNP) distributions for leveraged exchange trade funds, (L)ETFs. We applied the SNP model with dynamic conditional correlations (DCC) and EGARCH innovations, and implement recent techniques to backtest Expected Shortfall (ES) to portfolios formed by bivariate combinations of major (L)ETFs on metal (Gold and Silver) and energy (Oil and Gas) commodities. Results support that multivariate SNP-DCC model outperforms the Gaussian-DCC and provides accurate risk measures for commodity (L)ETFs.
... For example, leveraged ETFs were blamed in the 1% run-up in the last 18 minutes of trade of the S&P 500 on October 10, 2011, despite the absence of any news (Sorkin 2011). According to Cheng & Madhavan (2009), the dynamics of leveraged ETFs lead to same-direction rebalancing (even for bear funds), akin to portfolio insurance. They also argue that short-term speculators are attracted to these products because they allow traders to make short-term, highly leveraged bets. ...
... When it is the converse, namely borrowing on the risky asset to increase the amount invested on the riskless one, the fund is usually called an "inverse leveraged ETF". Cheng and Madhavan (2009) show how inverse ETFs need to be rebalanced on a daily basis to maintain a constant leverage. Charupat and Miu (2011) state that frequent rebalancing of leveraged ETF portfolios for periods of high volatility is necessary so that leveraged exposure to the tracked index could be maintained. ...
Article
In this paper, we examine if, for a successful long-term investment of leveraged ETFs, it is necessary to adjust the level of leverage according to the fluctuations of the financial markets. For this purpose, we illustrate in particular the behavior of the Leverages ETF based on the optimal leverage introduced by Giese (2009). This latter one, which is based on the growth rate expectation, behaves as a function of the prevailing market environment. More precisely, it implies that the investor should use high leverage in low volatility markets and low leverage in high volatility markets. We study also how the degree of leverage depends on the main factor of market environment, namely the volatility of the market in force.
... Ramaswamy (2011) examines the operational frameworks of exchange-traded funds and relates these to potential systemic risks. The role of leveraged ETFs has also been discussed (for example,Cheng and Madhavan 2009) in the context of end-of-day volatility effects. ...
Article
Exchange-traded funds (ETFs) represent one of the most important financial innovations in decades. An ETF is an investment vehicle, with a specific architecture that typically seeks to track the performance of a specific index. The first US-listed ETF, the SPDR, was launched by State Street in January 1993 and seeks to track the S&P 500 index. It is still today the largest ETF by far, with assets of $178 billion. Following the introduction of the SPDR, new ETFs were launched tracking broad domestic and international indices, and more specialized sector, region, or country indexes. In recent years, ETFs have grown substantially in assets, diversity, and market significance, including substantial increases in assets in bond ETFs and so-called “smart beta” funds that track certain investment strategies often used by actively traded mutual funds and hedge funds. In this paper, we begin by describing the structure and organization of exchange-traded funds, contrasting them with mutual funds, which are close relatives of exchange-traded funds, describing the differences in how ETFs operate and their potential advantages in terms of liquidity, lower expenses, tax efficiency, and transparency. We then turn to concerns over whether the rise in ETFs may raise unexpected risks for investors or greater instability in financial markets. While concerns over financial fragility are worth serious consideration, some of the common concerns are overstated, and for others, a number of rules and practices are already in place that offer a substantial margin of safety.
... These counterparts, despite the fact that both have the same reference the junior gold miners ETF (GDXJ; Van Eck, 2017) in exactly the same percentage ratio but in an opposite manner (i.e. +3x -3x), actually both follow a constantly declining price action procedure and this strange behave, explained statistically by local-stochastic volatility models (see Cheng & Madhavan, 2009;Avellaneda & Zhang, 2010), is a typical technical market anomaly. In fact, in computational finance theory, leveraged (ETF) implied volatility from (ETF) dynamics (Leung et al., 2015). ...
Article
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The main goal of this paper is to introduce the leveraged ETF die-down price action technical market anomaly (leveraged ETF anomaly), and then to discuss the temporal dimension and the subsequent (time-series) functionalities of this anomaly (temporal leveraged ETF anomaly). Our approach not only challenging the efficient-market hypothesis with regards to constantly declining leveraged ETF price action course, but also has a temporal dimension because it uses the Jesse Livermore’s “psychological time” as parameter in both functions: (i) “emotional control” for opening position at the beginning of an intraday or short-term move and thereafter for holding this position; and (ii) in “money risk management - exit policy” for closing position. Traditional fundamental analysis theories and technical analysis rules and approaches are not able to interpret the die-down (i.e. a constantly declining in a mid- and long-term basis) leveraged ETF price action course. Instead, a rational dynamic and temporal representative agent could explain and document better this anomaly and this is the case of this article (i.e. trading exploitation functionality). The presented research shows that the proposed temporal leveraged ETF anomaly accumulates profit entirely overnight in sideways and in choppy markets, while in a trending market the profit occurs intraday. These findings for the leveraged ETF instruments reject classical theories of trending and sideways markets returns. Hence, (i) in a sideways or in a choppy market, a well designed overnight-position return strategy based on temporal leveraged ETF anomaly; and (ii) in a trending market, a well designed daytime-position return strategy based on temporal leveraged ETF anomaly as well, could gain benefit at the expense of hedgers and long-term investors respectively. After back-testing our research in available 5-year data for the JNUG 3x leveraged ETF (gold miners juniors), we found that overnight-position speculators, in sideways or choppy markets, profit from the proposed temporal leveraged ETF trading strategy approach at the expense of hedgers; and daytime swing traders, in trending markets, profit from the proposed temporal leveraged ETF trading strategy approach at the expense of long-term investors.
... LIP investment amount, whereas direct short selling leads to a potentially unlimited investor liability. A well-known drawback of LIPs is volatility drag or volatility decay, the tendency of volatility to decrease compound returns over longer periods (Cheng and Madhavan 2009;Charupat and Miu 2016). Volatility drag is also known as beta slippage or beta decay (Trainor 2011). ...
Article
Volatility reduces any investment’s compound rate of return in what is termed “volatility drag,” a drawback of leveraged investment products (LIPs). In recent years “Version 2.0” LIPs that reset leverage monthly (monthly LIPs) have been created to lessen the impact of drag. We show that monthly LIPs improve returns because markets are less volatile on a monthly timescale. Nevertheless, monthly LIPs remain problematic as buy-and-hold investments due to the risks of large drawdowns and catastrophic losses. We characterize these risks through higher-order moments and identify attributes of LIPs to mitigate these risks to benefit both LIP investors and LIP sponsors.
... Intuitively, these end-of-day flows of leveraged ETFs may positively affect liquidity and volatility of component stocks. Indeed, Cheng and Madhavan (2009) develop a model, showing that the rebalancing of leveraged ETFs has a large impact on market-on-close volume, liquidity and volatility of the underlying securities. Moreover, the effects are proportional to the assets invested in leveraged ETFs. ...
Article
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Exchange-traded funds (ETFs) belong to the fastest growing investment products worldwide. Within 15 years, total assets invested in ETFs have twenty-folded, reaching over $3.7 trillion at the end of 2018. Increasing demand for passive investments, coupled with high liquidity and low transaction costs, are key advantages of ETFs compared to their closest substitutes such as traditional index funds. Besides the continuous growth of ETFs, the Flash Crash in 2010 triggered detailed investigations by regulators on how ETFs affect the financial market. This literature review provides a broad overview of recent academic studies analyzing the effect of ETFs on liquidity, price discovery, volatility, and comovement of the underlying securities.
... Several studies further discuss whether leveraged ETFs intensify end-of-day market volatility. On one hand, Cheng and Madhavan (2009), Charupat and Miu (2011), and Shum et al. (2016 show that the end-of-day rebalancing of funds' exposures increases trading volume and market volatility at the close of a trading day. On the other hand, Ivanov and Lenkey (2018) find that the impact of ETF rebalancing on lateday volatility is economically insignificant when capital flows and standard risk factors are taken into account. ...
Article
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This study aims to investigate the day‐of‐the‐week effect of cross‐market leveraged exchange‐traded funds (LETFs) in the Taiwanese stock market. We find that Wednesday's overnight returns are significantly positive for bull 2X LETFs tracking major stock indices of the Chinese market, whereas no such an effect is found for ETFs tracking local or other international stock markets. The “T + 1” trading rule and a lagged Monday effect potentially explain this anomaly. Finally, simulation analysis of various simple trading rules further shows that there exist exploitable profit opportunities in cross‐market bull 2X LETF markets.
... 19 These strategies can be employed in a variety of investment vehicles, including vehicles that are not SEC-registered investment companies, although most of the academic literature has focused on their use among a relatively small group of ETFs. Cheng and Madhavan (2009) and Tuzun (2014) show that leveraged and inverse ETFs (LETFs, or "geared" ETFs) -which seek daily returns that are, respectively, positive and negative multiples of an underlying index return -both must trade in the same direction as market moves that occurred earlier in the day. 20 That is, so-called "geared" passive investment strategies cause both leveraged and inverse ETFs to buy assets (or exposures via swaps or futures) on days when asset prices rise, and sell when the market is down. ...
... However, the returns that are larger than the average can be a lot larger. Cheng and Madhavan (2009) showed that under certain circumstances the long term returns can be significantly below that of the appropriately levered underlying index. This is particularly true for volatile indices and for IETFs. ...
... 19 These strategies can be used in a variety of investment vehicles, including vehicles that are not SEC-registered investment companies, although most of the academic literature has focused on their use among a relatively small group of ETFs. Cheng and Madhavan (2009) and Tuzun (2014) showed that leveraged and inverse ETFs (LETFs, or "geared" ETFs)-which seek daily returns that are, respectively, positive and negative multiples of an underlying index return-both must trade in the same direction as market moves that occurred earlier in the day. 20 That is, so-called geared passive investment strategies cause both leveraged and inverse ETFs to buy assets (or exposures via swaps or futures) on days when asset prices rise and to sell assets when the market is down. ...
Article
The past two decades have seen a significant shift from active to passive investment strategies. We examined how this shift affects financial stability through its impacts on (1) funds’ liquidity and redemption risks, (2) asset market volatility, (3) asset management industry concentration, and (4) comovement of asset returns and liquidity. Overall, the shift appears to be increasing some risks and reducing others. Some passive strategies amplify market volatility, and the shift has increased industry concentration but has diminished some liquidity and redemption risks. Evidence on the links between indexing and comovement of asset returns and liquidity is mixed.
Chapter
This chapter illustrates and explains the biases, anomalies and problems inherent in Leveraged/Inverse EFTs and Synthetic ETFs/Funds which often have tracking errors and misleading advertising, but are considered to be an improvement over leveraged mutual funds. A group of asset management companies, including Direxion and ProShares, have launched Leveraged/Inverse ETFs that focus on specific markets around the world. As of 2018, more than the equivalent of USD$500 billion had been invested in Leveraged/Inverse ETFs and Synthetic ETFs/Funds worldwide. However, the advertised terms of most Leveraged/Inverse ETFs (such as the ProShares leveraged/Inverse ETFs) and Synthetic ETFs/Funds are inaccurate and grossly misleading.
Article
The terms of exchange‐traded stock option contracts are usually adjusted when corporate actions take place. These adjustments are made to safeguard the value of the outstanding option contracts. Recently, a new type of corporate event has appeared − levered and inverse exchange‐traded product issuers are reducing leverage ratios with increased frequency. While such changes directly affect option values, no contract adjustments are made, resulting in windfall transfers of wealth from outstanding long to outstanding short option holders. In one instance alone, the transfer was more than $US100 million. To remedy the problem, we offer a simple contract adjustment procedure.
Article
New ETF creation has surged in recent years, giving investors the option to choose from a wide range of similar ETFs within each group of competitors. We identify groups of ETFs that can be considered direct competitors and examine the impact of competition on their market quality. Results show improved market quality measures when competition increases. A change equivalent to going from a monopoly to a highly competitive market results in a 29% decrease in bid–ask spreads, a 72% decrease in illiquidity, and a 52% increase in turnover. However, we find that competition has a differential impact on ETFs according to their market depth. Market quality improves with competition for large or well-performing ETFs, while it worsens for small or under-performing ETFs. A case study on ETFs banned by the SEC in March 2010 further highlights our results in the artificially controlled competitive environment of the moratorium.
Article
Hedging short gamma exposure requires trading in the direction of price movements, thereby creating price momentum. Using intraday returns on over 60 futures on equities, bonds, commodities, and currencies between 1974 and 2020, we find strong market intraday momentum everywhere. The return during the last 30 minutes before the market close is positively predicted by the return during the rest of the day (from previous market close to the last 30 minutes). The predictive power is economically and statistically highly significant, and reverts over the next days. We provide novel evidence that links market intraday momentum to the gamma hedging demand from market participants such as market makers of options and leveraged ETFs.
Article
This paper examines the performance of monthly-rebalanced Leveraged Exchange-Traded Products (LETPs), and compares the performance and mandatory rebalancing needs between monthly-rebalanced LETPs and daily-rebalanced LETPs. We find that our sample monthly-rebalanced LETPs can approximately deliver their stated multiples. The monthly-rebalanced LETPs still suffer from compounding effect when holding period is multiple months, but this effect is mitigated relative to daily-rebalanced LETPs. Investors can gain a predictable return multiple different from the stated multiple by purchasing monthly-rebalanced LETPs at a non-rebalancing time. Even after controlling for the underlying index, holding period, and target return multiple, the performance and risks of monthly-rebalanced LETPs are much different from those of daily-rebalanced LETPs. In addition, the monthly LETPs generally require more mandatory rebalancing than the daily ones. These findings help investors, practitioners, and regulators understand the performance behaviors and potential consequences of monthly-rebalanced LETPs.
Article
Using the most comprehensive data set of leveraged funds known to the literature, we measure the market‐wide shadow cost of leverage constraints and examine its pricing implications. The shadow cost averages 0.53% per annum from 2006 to 2016, spikes upon quarter‐ends when banks face tighter capital requirements, positively predicts future betting‐against‐beta (BAB) returns, and negatively correlates with contemporaneous BAB returns. Stocks that experience lower returns when the shadow cost increases earn 0.85% more per month. Overall, our shadow cost measure fits the predictions of leverage‐constraint‐based theories better than the widely used TED spread. This article is protected by copyright. All rights reserved
Article
The emergence of energy commodity exchange-traded fund (ETFs) has provided an alternative vehicle for both energy commodity users (long hedgers) and producers (short hedgers) to hedge their respective exposures to unfavorable commodity energy price movements without opening a relatively expensive futures account. This paper examines the usefulness of ETFs in dealing with tail risk in crude oil, gasoline, heating oil, and natural gas markets by analyzing the out-of-sample hedging effectiveness of ETFs and comparing their performance with those of the futures counterparts. The empirical distribution method and kernel copula method are applied to estimate the minimum-Value at Risk (VaR) and minimum-Expected Shortfall (ES) hedge ratios for both long and short hedgers. Our results indicate that the futures contract is a better hedging instrument for hedging tail risk in the crude oil and heating oil markets whereas the ETF provides better downside risk protection in the gasoline and natural gas markets.
Chapter
This chapter is designed to provide theoretical framework for the empirical research regarding development of ETFs markets. The special emphasis is to put on the innovative funds in the Asia-Pacific region. It discusses the basic mechanisms of ETFs, showing the role of various participants of the ETFs markets and distinguishing between primary and secondary market. It compares ETFs to their main alternative in the financial system—mutual funds—showing relative advantages and disadvantages of both categories. Additionally, key events of the ETFs’ history are described. After the introductory discussion, it presents the main categories of ETFs, classified according to the key criteria, including the replication method, distinction between passive and active funds, approaches to the rate of return in relation to their benchmarks, and types of underlying assets. The third part of the chapter is devoted to the discussion of the definition of the ETFs market development, comparisons between ETFs and stock index derivatives (with the focus on the stock index arbitrage complex), presentation of applications of ETFs, and providing some insights into the topic of the determinants of the ETFs market development. Finally, it discusses the main characteristics of the Asia-Pacific ETFs markets—it presents the summary of their history, main market development statistics (in terms of assets, number, and other attributes), their structure, and position of ETFs in the Asia-Pacific investment industries (compared to mutual funds).
Article
The optimal return magnification of an exchange traded product relative to the returns of its underlying security can increase its profitability
Book
This book is dedicated to examining Exchange-Traded Funds (ETFs) market in the Asia-Pacific region between 2004 and 2017. It offers a broad examination of the attributes and development of the ETF markets. The book presents a new approach to ETF markets modeling that uses innovation diffusion model. In addition, it explores the empirical links between ETFs and Information and Communication Technologies (ICTs). The book also compares ETFs and competing investment options. This book should appeal to both academics and practitioners as it includes detailed descriptions of the ETF markets and prepared projections regarding their future development. As the Asia-Pacific region plays a significant role in the global economy, this book should be useful for international readers beyond this area. The Emergence of ETFs in Asia-Pacific begins with an overview of the Asia-Pacific economies, focusing on their importance for the global economy and their features. Next, the book introduces an analytical framework. It explains major features of ETFs (such as their creation, distribution, and trading) and key categories, which facilitates profound understanding of the book merit even for readers with little knowledge about ETFs. The following chapter explores the role of ICTs in economy and society identifying channels of their impact on financial markets. It discusses how ICTs foster dynamic spread of financial innovations (including ETFs) across financial markets. Next, the book examines the ETF market's development in different countries in the Asia-Pacific region, by analyzing their level of development in terms of turnover. In this part it also provides brief characteristics of all markets, including their structures and categories of ETFs in various countries. Consecutive part of the book is dedicated to reports on the process of ICTs growing penetration across Asia-Pacific countries, showing the changes observed during recent years. It then continues the empirical analysis of the ETF markets in the Asia-Pacific region by attempting to trace the links between the development of ETF markets and ICT penetration during the period 2004-2017. As complementary material, a methodological annex is included showing major analytical techniques used throughout the research.
Chapter
This chapter comprises results of the empirical analysis of ETFs markets in the Asia-Pacific region. It provides an overview of the current state of development of ETFs markets in 12 countries. First, it presents and compares their level of development and provides short characteristics, including their structures and features of the key categories of ETFs used in various countries. Moreover, it describes the main trends of the Asia-Pacific regional ETFs market in terms of turnover (and number of listed funds), supplemented by the analysis of the inequalities concerning diffusion of ETFs in the region. Second, this chapter demonstrates the results regarding ETFs diffusion, i.e., ETFs market development that is considered in two perspectives: as the value of turnover of ETFs on the local exchanges (absolute approach) or as the share of ETFs in the total turnover of index instruments (relative approach). The analysis is conducted using the models of diffusion of innovation. The final part of the chapter is devoted to discussion of projections of the diffusion of ETFs in the Asia-Pacific region. Calculations are based on monthly data for the years 2004–2017.
Article
This paper examines the differences between leveraged and unleveraged Exchange Traded Funds (ETFs), particularly for liquidity and volatility characteristics. The impact of leverage on intraday liquidity (spread and depth) is analysed in two periods – one of normal volatility and the other of abnormal/high volatility. There is a significant difference in spread and depth of leveraged and unleveraged ETFs in periods of both normal volatility and high volatility; however, this difference is more pronounced in higher volatility periods. In high volatility periods, liquidity typically diminishes in all ETFs, and this is even more so for the leveraged ETFs. When leveraged ETFs are segregated into multiples based on their power to replicate the underlying benchmark (i.e. multiples of −3, −2, −1, 2, 3), the difference in spreads between normal and high volatility periods is typically larger. The double-leveraged ETF has the most significant difference between the positive and negative counter parts. However, the relationship in the progression of the multiples does not change linearly to correspond with the level of volatility. This may be due to the nonlinear relation between volume and volatility. We shed light on the magnification effect of financial leverage on microstructure of the ETFs.
Article
What is the market impact of predictable order flow? Leveraged exchange-traded products are useful for answering this question because they generate daily rebalancing flows whose size, sign and timing are predictable. This paper presents new evidence from the market for leveraged volatility products. While the daily rebalancing imposes an implicit cost on investors by putting pressure on closing prices, there is no evidence that the cost is driven by predatory trading. On the contrary, I show that larger and more predictable flows have smaller price impact coefficients, and that there are no excess profits from trading ahead of rebalancing flows during the sample period.
Article
We investigate the effect of exchange-traded fund (ETF) liquidity on ETF tracking errors, returns, and volatility in the US. We find that illiquid ETFs have large tracking errors. The effect is more pronounced when underlying assets are less liquid. Returns and liquidity of illiquid ETFs are more sensitive to underlying index returns or ETF market liquidity, or both. Thus, a positive liquidity premium exists in US ETF markets. The ETF variance could be larger than its net asst value variance owing to infrequent trading. In summary, illiquid ETFs are more likely to deviate from their underlying indexes and could be riskier than underlying portfolios.
Chapter
Full-text available
This chapter focuses on the client–operator relationship in a Bank of the Credito Cooperativo system (BCC; Mutual Bank thereafter), a bank characterized by a strong link with the territorial identity, interlocked with a particular activation of trust in the face-to-face client–operator interaction in the branches. Following the mutuality rules, all the BCC banks have to respect territorial boundaries. Moreover, they have few decisional levels and a simple organizational structure. These elements facilitate the ‘embeddedness’ of operators in the social and economic context in which they operate. The possibility for clients to become members, a low standardisation, a contained use of ITC in risk assessment and in sharing information on financial products, are the main features that configure the situated interactions between client and operator.
Chapter
This chapter discusses trading strategies for exchange-traded funds (ETFs), including detailed mathematical descriptions. Momentum-based strategies include sector momentum rotation, which can be augmented with a filter based on moving averages. Another momentum strategy is based on dual-momentum sector rotation, which utilizes both cross-sectional momentum and time-series momentum. The chapter also discusses other strategies such as those based on ETF alpha rotation with alphas obtained using a serial regression against the three Fama–French factors, cross-sectional R-squared also known as “selectivity” obtained using the residuals of a serial regression against the three Fama–French factors plus Carhart’s momentum factor, mean-reversion using internal bar strength (IBS), arbitraging a long-run negative drift in leveraged ETFs by shorting a leveraged ETF and a leveraged inverse ETF, and multi-asset trend-following strategies using ETFs.
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